Sort data frame by values of character string in column in R

I have dataset like this:

term occ value
Less Than 1 year Yale 1
Less Than 1 year MIT 3
1 Year Yale 2
2 Years Yale 3
2 Years Yale 8
2 years CMU 2
3 Years Yale 5
3 years NYU 2
Greater than 3 Years NYU 5
Greater Than 3 Years CALTEC 4
No Fixed Term Yale 2
Other Bu 9

I want a table shows counts of the numbers of records by Term. And table should be in order of Term.

NOTE: The difference between "Years" and "years", "Than" and "than".

The output is like this:

term count
Less Than 1 year 2
1 Year 1
2 Years 3
3 Years 2
Greater than 3 Years 2
No Fixed Term 1
Other 1